Question: Simplify the following expression: $ n = \dfrac{9}{x - 3} + \dfrac{-4}{7} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{9}{x - 3} \times \dfrac{7}{7} = \dfrac{63}{7x - 21} $ Multiply the second expression by $\dfrac{x - 3}{x - 3}$ $ \dfrac{-4}{7} \times \dfrac{x - 3}{x - 3} = \dfrac{-4x + 12}{7x - 21} $ Therefore $ n = \dfrac{63}{7x - 21} + \dfrac{-4x + 12}{7x - 21} $ Now the expressions have the same denominator we can simply add the numerators: $n = \dfrac{63 - 4x + 12}{7x - 21} $ $n = \dfrac{-4x + 75}{7x - 21}$